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Questions and Answers
What is a variable?
What is a variable?
What is a constant?
What is a constant?
A quantity that does not change
Define an algebraic expression.
Define an algebraic expression.
An expression that contains one or more variables and may contain operation symbols
What does it mean to evaluate an expression?
What does it mean to evaluate an expression?
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What is an equation?
What is an equation?
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What is a solution in algebra?
What is a solution in algebra?
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What are inverse operations?
What are inverse operations?
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The order of operations is a rule for evaluating expressions: first perform the operations in ______, then find the values of numbers with exponents, then multiply or divide from left to right, and then add or subtract from left to right.
The order of operations is a rule for evaluating expressions: first perform the operations in ______, then find the values of numbers with exponents, then multiply or divide from left to right, and then add or subtract from left to right.
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What is the Commutative Property?
What is the Commutative Property?
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What is the Associative Property?
What is the Associative Property?
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What does the Distributive Property state?
What does the Distributive Property state?
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What is the Identity Property?
What is the Identity Property?
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What is an exponent?
What is an exponent?
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Define the base in an exponential expression.
Define the base in an exponential expression.
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What is exponential form?
What is exponential form?
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Study Notes
Key Terms in Algebra
- Variable: A letter or symbol representing a quantity that can change within mathematical expressions.
- Constant: A fixed quantity that does not vary.
- Algebraic Expression: A combination of one or more variables and constants linked by operation symbols (e.g., addition, subtraction).
Fundamental Operations and Concepts
- Evaluate: The process of substituting a specific number for a variable in an expression and simplifying to find its value.
- Equation: A mathematical assertion that asserts two quantities are equal, often containing variables.
- Solution: A specific value of a variable that satisfies an equation and makes it valid.
Properties of Operations
- Inverse Operations: Operations that reverse the effect of each other, such as addition and subtraction or multiplication and division.
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Order of Operations: A prescribed sequence for evaluating mathematical expressions:
- Parentheses first
- Exponents second
- Multiplication and division from left to right
- Addition and subtraction from left to right
Algebraic Properties
- Commutative Property: Demonstrates that the order of addition or multiplication does not influence the result; e.g., a + b = b + a.
- Associative Property: Indicates that the grouping of numbers does not affect the sum or product when adding or multiplying; e.g., (a + b) + c = a + (b + c).
- Distributive Property: When distributing multiplication over addition, multiplying a sum by a number yields the same result as multiplying each addend individually and then summing them; expressed as a(b + c) = ab + ac.
Identity Elements
- Identity Property: Defines that adding zero to a number yields the number itself, and multiplying a number by one results in the number unchanged.
Exponents
- Exponent: A notation that signifies how many times a base is multiplied by itself.
- Base: The number being multiplied in an exponential expression.
- Exponential Form: Expressing numbers using a base and an exponent to indicate repeated multiplication.
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Description
Explore fundamental concepts in algebra with these flashcards. Each card presents key terms along with concise definitions to enhance your understanding of variables, constants, and algebraic expressions. Perfect for beginners looking to grasp the basics of algebra.
